Comparative statics for rank-dependent expected utility theory

Recently, a number of generalizations of the expected utility (EU) model have been proposed. In order to make such generalizations useful, it is necessary that they should yield sharp comparative static results, like those obtained using EU theory. In this article, rank dependent expected utility (RDEU) theory, a generalization of EU theory based on the concept of probability weighting, is examined. A number of methods of extending results from EU to RDEU are considered. It is shown that a major class of comparative static results can be extended to the RDEU model, but not to the case of general smooth preferences. This is because RDEU maintains the separation between probabilities and utilities that is abandoned in the general case.

[1]  Mark J. Machina,et al.  Comparative Statics and Non-expected Utility Preferences* , 1989 .

[2]  L. J. Savage,et al.  The Utility Analysis of Choices Involving Risk , 1948, Journal of Political Economy.

[3]  Jack Meyer,et al.  Deterministic transformations of random variables and the comparative statics of risk , 1989 .

[4]  I. Gilboa.  Expected utility with purely subjective non-additive probabilities , 1987 .

[5]  Joseph E. Stiglitz,et al.  The Theory of Commodity Price Stabilization: A Study in the Economics of Risk. , 1983 .

[6]  Agnar Sandmo,et al.  The Effect of Uncertainty on Saving Decisions , 1970 .

[7]  Agnar Sandmo,et al.  "Fixed Costs" and the Competitive Firm Under Price Uncertainty: Reply , 1972 .

[8]  M. Rothschild,et al.  Increasing risk II: Its economic consequences , 1971 .

[9]  Mark J. Machina,et al.  Temporal risk and the nature of induced preferences , 1984 .

[10]  J. Quiggin.  Subjective utility, anticipated utility, and the Allais paradox , 1985 .

[11]  John Quiggin,et al.  Risk Perception And The Analysis Of Risk Attitudes , 1981 .

[12]  Larry G. Epstein,et al.  A correspondence theorem between expected utility and smooth utility , 1988 .

[13]  M. Allais,et al.  The General Theory of Random Choices in Relation to the Invariant Cardinal Utility Function and the Specific Probability Function. The (U, θ) Model A General Overview , 1988 .

[14]  W. Viscusi.  Prospective reference theory: Toward an explanation of the paradoxes , 1989 .

[15]  A. Sandmo.  On the theory of the competitive firm under price uncertainty , 1971 .

[16]  J. Quiggin.  ON THE OPTIMAL DESIGN OF LOTTERIES , 1991 .

[17]  Donald V. Coes.  Firm Output and Changes in Uncertainty , 1977 .

[18]  S. Chew.  A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox , 1983 .

[19]  J. Quiggin.  A theory of anticipated utility , 1982 .

[20]  John Quiggin,et al.  Increasing Risk: Another Definition , 1991 .

[21]  M. Yaari.  The Dual Theory of Choice under Risk , 1987 .

[22]  Uday S. Karmarkar,et al.  Subjectively weighted utility: A descriptive extension of the expected utility model , 1978 .

[23]  C. S. Hong,et al.  Risk aversion in the theory of expected utility with rank dependent probabilities , 1987 .

[24]  J. Lintner.  THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS , 1965 .

[25]  K. Arrow,et al.  Uncertainty and the Evaluation of Public Investment Decisions , 2014 .

[26]  Uzi Segal,et al.  SOME REMARKS ON QU|GGIN'S ANTICIPATED UTILITY* , 1986 .

[27]  A. Tversky,et al.  Prospect theory: analysis of decision under risk , 1979 .

[28]  M. Machina.  "Expected Utility" Analysis without the Independence Axiom , 1982 .

[29]  Gershon Feder,et al.  The impact of uncertainty in a class of objective functions , 1977 .

[30]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

[31]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

[32]  Dimitri P. Bertsekas,et al.  Necessary and sufficient conditions for existence of an optimal portfolio , 1974 .

[33]  D. Schmeidler.  Subjective Probability and Expected Utility without Additivity , 1989 .

[34]  Edi Karni,et al.  Preference reversal and the observability of preferences by experimental methods , 1987 .

[35]  James Tobin,et al.  Comment on Borch and Feldstein , 1969 .

[36]  Uzi Segal.  Anticipated utility: A measure representation approach , 1989 .

[37]  A Note on the Existence of a Competitive Optimal Output , 1982 .

[38]  W. Sharpe.  CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK* , 1964 .

[39]  J. Stiglitz,et al.  Increases in risk and in risk aversion , 1974 .

[40]  Ventures, Bets and Initial Prospects , 1972 .